Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal subgraphs that satisfy specific density and similarity thresholds. To measure the similarity of the temporal behavior, we use the correlation between the binary time series that represent the activity of the edges. For the density, we study two variants based on the average degree. For these problem variants we enumerate the maximal subgraphs and compute a compact subset of subgraphs that have limited overlap. We propose an approximate algorithm that scales well with the size of the network, while achieving a high accuracy. We evaluate our framework on both real and synthetic datasets. The results of the synthetic data demonstrate the high accuracy of the approximation and show the scalability of the framework.

中文翻译：

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在动态网络中发现密集相关子图

给定一个动态网络，其中边缘随时间出现和消失，我们有兴趣寻找具有相似时间行为并形成密集子图的边缘集。形式上，我们将问题定义为满足特定密度和相似性阈值的最大子图的枚举。为了测量时间行为的相似性，我们使用表示边缘活动的二进制时间序列之间的相关性。对于密度，我们根据平均程度研究了两个变体。对于这些问题的变体，我们枚举了最大的子图，并计算了具有有限重叠的子图的紧凑子集。我们提出了一种近似算法，该算法可以随着网络的大小而很好地扩展，同时又可以实现较高的精度。我们在真实和综合数据集上评估我们的框架。